hmmmmmmm
Maybe you should throw in some values (positive and negative) as that would certainly classify as proof.
1a) Let x = 1, p = 2, q = 3
1²*1³ = 1, 15 = 1 therefore
Let x = -2, p = 2, q = 3
-2²*-2³ = -32, -25 = -32 therefore
1b) Let x = 1, p = 2, q = 3
1²/1³ = 1, 1-1 = 1 therefore
Let x = -2, p = 2, q = 3
-2²/-2³ = -0.5, -2-1 = -0.5 therefore
1c) Let x = 1, y = 2, p = 3
1³*2³ = 8, (1*2)³ = 8 therefore
Let x = -2, y = 3, p = 3
-2³*3³ = -216, (-2*3)³ = -216 therefore
If you prefer you can use your own values as long as one is negative and one is positive. This would definitely class as proof as far as i can see.
Hope this helps.